1. Field of the Invention
The present invention applies notably to the field of electronic lithography for direct etching on a wafer or for fabricating masks. More generally, it applies to any field in which there is a need to model the interaction of an electron beam with a target, which is also the case in electronic microscopy, notably for the inspection of the wafers and of the masks.
2. Description of the Related Art
The interaction of an electron beam with a target is notably affected by a scattering of the electrons around the initial trajectory (forward scattering effect) and by a back-scattering effect. These effects, termed proximity effects, depend notably on the materials of the target and on its geometry. Whatever the reason for wanting to perform this electronic bombardment (etching, imaging or analysis), it is therefore necessary to take account of the proximity effects in order to obtain a result which is true to the desired objective. A correction of the proximity effects is therefore performed. For this, it is known practice to predict them using a model in order to take them into account in calculating the doses of electronic radiation used to bombard the target. For this, it is a known practice to use a so-called scattering or point spread function (PSF) and a convolution of the PSF with the geometry of the target is performed. A PSF that is commonly used is a combination of Gaussians, a first Gaussian to model the forward scattering (PSF of the forward scattering), and one or more additional Gaussians to model the backscattering (PSF of the backscattering).
The PSF equation is thus conventionally represented by a function f(x,y) of the following form:
      f    ⁡          (      ξ      )        =            1              π        ⁡                  (                      1            +            η                    )                      ⁢          (                                    1                          α              2                                ⁢                      ⅇ                                          -                                  ξ                  2                                                            α                2                                                    +                              η                          β              2                                ⁢                      ⅇ                                          -                                  ξ                  2                                                            β                2                                                        )      
With the following notations:                α is the width of the direct radiation;        β is the backscattering width;        η is the ratio of the intensities of the direct and backscattered radiations;        ξ is the radial position of a point.        
The values of the parameters α, β and η can be determined by trial and error for a given process. These parameters are a function of the acceleration voltage of the machine and of the target. Typically, for an acceleration voltage of the order of 50 KV and a silicon or glass target (SiO2), α is of the order of 30 nm, β of the order of 10 μm and ƒ of the order of 0.5.
The efficiency of this model is, however, not good, notably for the distant effects which are dominated by backscattering. Other PSFs can be used to obtain better efficiencies, notably those of the type suggested by Kamikubo in “Mask Process Correction (MPC) modeling and its application to EUV mask for Electron beam mask writer, EBM-7000”, Photomask Technology, Proc. of SPIE, Vol. 7823, 782331, 2010, or the model suggested by Belic in U.S. patent application publication no. 2008/067466. Kamikubo suggests the use of a PSF comprising an exponential function and demonstrates an improvement compared to the Gaussian model. Belic presents a model comprising a linear combination of a number of Gaussian functions, one or more of the coefficients of the linear combination being possibly negative in order to better fit the PSF to physical reality. It has, however, been found that these two variants of the standard functional form of the PSF—the performance of which can be evaluated both by trial and error and by comparison with a model simulating the scattering of the electrons by the Monte-Carlo method (hereinafter in the description termed reference model)—bring improvements that are still insufficient at afar field, notably in applications of the type including mask etching in extreme UV (ultraviolet), said masks generally comprising layers of heavy metals such as tantalum. One of the common features of the PSFs of the prior art is to use centered functions, that is to say, functions for which the maximum amplitude is located where the center of the electronic beam interacts with the target (for the sake of simplicity, this will hereinafter be referred to as at the center of the beam); now, this model is not a good fit with reality, notably in the application scenarios described above in which the proportion of backscattering is significant.